{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "1D_infinite domain_Analytical.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNNr14wv7UTe+DL2fhDlpfH",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Divyanshu-ISM/Oil-and-Gas-data-analysis/blob/master/1D_infinite_domain_Analytical_to_do.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ugwIaxgJ2QJx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sympy import *\n",
        "\n",
        "%matplotlib inline"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zjvBKuiE2nz3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "k_md = 50\n",
        "k_m2 = k_md*0.987E-15\n",
        "\n",
        "phi = 0.25\n",
        "\n",
        "ct_psi = 1E-03\n",
        "ct_pa = ct_psi*14.7/101325\n",
        "\n",
        "\n",
        "Mu_cp=3\n",
        "Mu_Pas=Mu_cp*10**(-3)\n",
        "\n",
        "diffusivity=k_m2/phi/Mu_Pas/ct_pa\n"
      ],
      "execution_count": 66,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9UkmNvCA2xCa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "q = 5 #bbls/day\n",
        "q_m3persec = q/6.29/(24*60*60)\n",
        "\n",
        "A = 5000 #m2\n",
        "\n",
        "alpha = q_m3persec*Mu_Pas/(k_m2*A)"
      ],
      "execution_count": 67,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O18sKTBUg0I2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "04e65b7a-6b86-4178-b324-03ad07054b29"
      },
      "source": [
        ""
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QkPA0l_b20Lo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "dx = 0.5\n",
        "x = np.arange(dx/2,10, dx)\n",
        "\n",
        "\n",
        "dt = 2\n",
        "t = np.arange(0,181,dt)\n",
        "\n",
        "beta = diffusivity*dt/dx**2\n",
        "\n",
        "\n",
        "\n"
      ],
      "execution_count": 68,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ymWYUX2coQMS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "b0ec69b6-dc12-4a4f-983b-25aba1ff8cea"
      },
      "source": [
        ""
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.25,  0.75,  1.25,  1.75,  2.25,  2.75,  3.25,  3.75,  4.25,\n",
              "        4.75,  5.25,  5.75,  6.25,  6.75,  7.25,  7.75,  8.25,  8.75,\n",
              "        9.25,  9.75, 10.25])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "doyxBHir4HWi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Pi = 205\n",
        "Pwf = 175\n",
        "\n",
        "# x_step = np.linspace(0,5,101)\n",
        "\n",
        "# t_step = np.linspace(0,1800,181)\n",
        "\n",
        "# P = np.ones((len(x_step),len(t_step)))"
      ],
      "execution_count": 70,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XP97rpQx7TqE",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "P = np.ones(len(x))*Pi"
      ],
      "execution_count": 69,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-IlnttQZ7j4Z",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 340
        },
        "outputId": "456cd789-6596-4e52-b40e-d77a234ee48a"
      },
      "source": [
        ""
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205., 205., 205., 205., 205., 205., 205., 205.,\n",
              "       205., 205., 205., 205.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DBcmDAUT8GT2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import math"
      ],
      "execution_count": 71,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-fTgD3tj5gv9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# for i  in range(1,len(x_step)):\n",
        "\n",
        "#   x = x + delta_x\n",
        "\n",
        "#   t=0;\n",
        "#   delta_t=10;\n",
        "\n",
        "#   for j in range(2,len(t_step)):\n",
        "\n",
        "#     t = t + delta_t\n",
        "\n",
        "#     Pr[i,j] = Pi - ((q_m3persec*Mu_Pas*(diffusivity**0.5)/k_m2/A)*(np.sqrt(t/np.pi)*np.exp(-1*x**2/4/diffusivity/t**2))\n",
        "#                   - (x*math.erfc(x/2/np.sqrt(diffusivity*t))/2/np.sqrt(diffusivity)))\n",
        "    \n",
        "\n"
      ],
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Fm77cME8t8v",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# from mpl_toolkits import mplot3d"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k0N_Umrw899S",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# fig = plt.figure()\n",
        "# ax = plt.axes(projection='3d')\n",
        "\n",
        "# ax.plot_surface(x, t, Pr,cmap='viridis', edgecolor='none')\n",
        "\n",
        "# ax.set_title('Pr in infinite domain plot')"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hMJv8-xAlKzI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pylab as pl\n",
        "from IPython import display\n",
        "import time"
      ],
      "execution_count": 72,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TQ0U3jHMogp9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "8ae8fdf2-bb8d-45cf-93c5-89a6937e3e67"
      },
      "source": [
        "x[-1]"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10.25"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9MOAfhhb9PLS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 669
        },
        "outputId": "6a10e75f-63a5-4a26-bd1a-46b59f8e9416"
      },
      "source": [
        "ax1 = plt.figure(figsize=(12,5))\n",
        "plt.grid()\n",
        "plt.style.use('fivethirtyeight')\n",
        "\n",
        "for j in t:\n",
        "\n",
        "  plt.clf()\n",
        "\n",
        "\n",
        "  for i in range(len(x)):\n",
        "\n",
        "    P[i] = Pi - alpha*np.sqrt(diffusivity)*(np.sqrt(j/3.14)*np.exp(-x[i]**2/4/diffusivity/j**2)  -  (x[i]/2/np.sqrt(diffusivity))*math.erfc(x[i]/2/np.sqrt(diffusivity*j)))\n",
        "  \n",
        "\n",
        "  plt.plot(x,P)\n",
        "\n",
        "  plt.xlim(dx/2 , x[-1]-dx/2)\n",
        "\n",
        "  \n",
        "  display.clear_output(wait=True)\n",
        "  display.display(pl.gcf())\n",
        "  time.sleep(1.0)"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R-Edv4cYlhkB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}